Correct Answer - Option 3 : 19 : 26
Given:
The ratio of the 10th term and the 12th term of an AP is 33 : 40.
The common difference is 4 more than the first term.
Formula Used:
n-th term of an AP = a + (n - 1) × d, where a is the first term, n is the total number of terms and d is the common difference.
Calculation:
(a + 9d)/(a + 11d) = 33/40
⇒ 40a + 360d = 33a + 363d
⇒ 7a = 3d
Now, d = 4 + a ----(1)
7a = 3 × (4 + a) [From (1)]
⇒ 7a = 12 + 3a
⇒ a = 3
From (1),
d = 4 + 3 = 7
The ratio of the 6th term to the 8th term = (a + 5d) : (a + 7d)
⇒ {(3) + 5(7)) : ((3) + 7(7)}
⇒ (3 + 35) : (3 + 49)
⇒ 38 : 52
⇒ 19 : 26
∴ Required ratio is 19 : 26
